toom4_sqr.c revision 1.1.1.1 
1/* mpn_toom4_sqr -- Square {ap,an}.
2
3   Contributed to the GNU project by Torbjorn Granlund and Marco Bodrato.
4
5   THE FUNCTION IN THIS FILE IS INTERNAL WITH A MUTABLE INTERFACE.  IT IS ONLY
6   SAFE TO REACH IT THROUGH DOCUMENTED INTERFACES.  IN FACT, IT IS ALMOST
7   GUARANTEED THAT IT WILL CHANGE OR DISAPPEAR IN A FUTURE GNU MP RELEASE.
8
9Copyright 2006, 2007, 2008, 2009, 2010 Free Software Foundation, Inc.
10
11This file is part of the GNU MP Library.
12
13The GNU MP Library is free software; you can redistribute it and/or modify
14it under the terms of the GNU Lesser General Public License as published by
15the Free Software Foundation; either version 3 of the License, or (at your
16option) any later version.
17
18The GNU MP Library is distributed in the hope that it will be useful, but
19WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
20or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General Public
21License for more details.
22
23You should have received a copy of the GNU Lesser General Public License
24along with the GNU MP Library.  If not, see http://www.gnu.org/licenses/.  */
25
26
27#include "gmp.h"
28#include "gmp-impl.h"
29
30/* Evaluate in: -1, -1/2, 0, +1/2, +1, +2, +inf
31
32  <-s--><--n--><--n--><--n-->
33   ____ ______ ______ ______
34  |_a3_|___a2_|___a1_|___a0_|
35
36  v0  =   a0             ^2 #    A(0)^2
37  v1  = ( a0+ a1+ a2+ a3)^2 #    A(1)^2   ah  <= 3
38  vm1 = ( a0- a1+ a2- a3)^2 #   A(-1)^2  |ah| <= 1
39  v2  = ( a0+2a1+4a2+8a3)^2 #    A(2)^2   ah  <= 14
40  vh  = (8a0+4a1+2a2+ a3)^2 #  A(1/2)^2   ah  <= 14
41  vmh = (8a0-4a1+2a2- a3)^2 # A(-1/2)^2  -4<=ah<=9
42  vinf=               a3 ^2 #  A(inf)^2
43*/
44
45#if TUNE_PROGRAM_BUILD
46#define MAYBE_sqr_basecase 1
47#define MAYBE_sqr_toom2   1
48#define MAYBE_sqr_toom4   1
49#else
50#define MAYBE_sqr_basecase						\
51  (SQR_TOOM4_THRESHOLD < 4 * SQR_TOOM2_THRESHOLD)
52#define MAYBE_sqr_toom2							\
53  (SQR_TOOM4_THRESHOLD < 4 * SQR_TOOM3_THRESHOLD)
54#define MAYBE_sqr_toom4							\
55  (SQR_FFT_THRESHOLD >= 4 * SQR_TOOM4_THRESHOLD)
56#endif
57
58#define TOOM4_SQR_REC(p, a, n, ws)					\
59  do {									\
60    if (MAYBE_sqr_basecase						\
61	&& BELOW_THRESHOLD (n, SQR_TOOM2_THRESHOLD))			\
62      mpn_sqr_basecase (p, a, n);					\
63    else if (MAYBE_sqr_toom2						\
64	     && BELOW_THRESHOLD (n, SQR_TOOM3_THRESHOLD))		\
65      mpn_toom2_sqr (p, a, n, ws);					\
66    else if (! MAYBE_sqr_toom4						\
67	     || BELOW_THRESHOLD (n, SQR_TOOM4_THRESHOLD))		\
68      mpn_toom3_sqr (p, a, n, ws);					\
69    else								\
70      mpn_toom4_sqr (p, a, n, ws);					\
71  } while (0)
72
73void
74mpn_toom4_sqr (mp_ptr pp,
75	       mp_srcptr ap, mp_size_t an,
76	       mp_ptr scratch)
77{
78  mp_size_t n, s;
79  mp_limb_t cy;
80
81#define a0  ap
82#define a1  (ap + n)
83#define a2  (ap + 2*n)
84#define a3  (ap + 3*n)
85
86  n = (an + 3) >> 2;
87
88  s = an - 3 * n;
89
90  ASSERT (0 < s && s <= n);
91
92  /* NOTE: The multiplications to v2, vm2, vh and vm1 overwrites the
93   * following limb, so these must be computed in order, and we need a
94   * one limb gap to tp. */
95#define v0    pp				/* 2n */
96#define v1    (pp + 2 * n)			/* 2n+1 */
97#define vinf  (pp + 6 * n)			/* s+t */
98#define v2    scratch				/* 2n+1 */
99#define vm2   (scratch + 2 * n + 1)		/* 2n+1 */
100#define vh    (scratch + 4 * n + 2)		/* 2n+1 */
101#define vm1   (scratch + 6 * n + 3)		/* 2n+1 */
102#define tp (scratch + 8*n + 5)
103
104  /* No overlap with v1 */
105#define apx   pp				/* n+1 */
106#define amx   (pp + 4*n + 2)			/* n+1 */
107
108  /* Total scratch need: 8*n + 5 + scratch for recursive calls. This
109     gives roughly 32 n/3 + log term. */
110
111  /* Compute apx = a0 + 2 a1 + 4 a2 + 8 a3 and amx = a0 - 2 a1 + 4 a2 - 8 a3.  */
112  mpn_toom_eval_dgr3_pm2 (apx, amx, ap, n, s, tp);
113
114  TOOM4_SQR_REC (v2, apx, n + 1, tp);	/* v2,  2n+1 limbs */
115  TOOM4_SQR_REC (vm2, amx, n + 1, tp);	/* vm2,  2n+1 limbs */
116
117  /* Compute apx = 8 a0 + 4 a1 + 2 a2 + a3 = (((2*a0 + a1) * 2 + a2) * 2 + a3 */
118#if HAVE_NATIVE_mpn_addlsh1_n
119  cy = mpn_addlsh1_n (apx, a1, a0, n);
120  cy = 2*cy + mpn_addlsh1_n (apx, a2, apx, n);
121  if (s < n)
122    {
123      mp_limb_t cy2;
124      cy2 = mpn_addlsh1_n (apx, a3, apx, s);
125      apx[n] = 2*cy + mpn_lshift (apx + s, apx + s, n - s, 1);
126      MPN_INCR_U (apx + s, n+1-s, cy2);
127    }
128  else
129    apx[n] = 2*cy + mpn_addlsh1_n (apx, a3, apx, n);
130#else
131  cy = mpn_lshift (apx, a0, n, 1);
132  cy += mpn_add_n (apx, apx, a1, n);
133  cy = 2*cy + mpn_lshift (apx, apx, n, 1);
134  cy += mpn_add_n (apx, apx, a2, n);
135  cy = 2*cy + mpn_lshift (apx, apx, n, 1);
136  apx[n] = cy + mpn_add (apx, apx, n, a3, s);
137#endif
138
139  ASSERT (apx[n] < 15);
140
141  TOOM4_SQR_REC (vh, apx, n + 1, tp);	/* vh,  2n+1 limbs */
142
143  /* Compute apx = a0 + a1 + a2 + a3 and amx = a0 - a1 + a2 - a3.  */
144  mpn_toom_eval_dgr3_pm1 (apx, amx, ap, n, s, tp);
145
146  TOOM4_SQR_REC (v1, apx, n + 1, tp);	/* v1,  2n+1 limbs */
147  TOOM4_SQR_REC (vm1, amx, n + 1, tp);	/* vm1,  2n+1 limbs */
148
149  TOOM4_SQR_REC (v0, a0, n, tp);
150  TOOM4_SQR_REC (vinf, a3, s, tp);	/* vinf, 2s limbs */
151
152  mpn_toom_interpolate_7pts (pp, n, 0, vm2, vm1, v2, vh, 2*s, tp);
153}
154